There's two main sets of numbers to remember:
1) focal length (focal lengths for zoom lenses)
2) maximum aperture (the size of the widest lens opening, which can vary slightly for zooms).
Let's start with focal lengths, which are a measure of how strong your lens is for wideness or telephoto. It allows you to make some relative comparisons between lenses. So, for example, let's say you have an 18-55mm lens. 18mm is fairly wide, while 55mm is a very moderate telephoto. By comparison, a 55-200mm lens goes from a moderate telephoto to a long telephoto.
Those are zoom lenses, which cover a range of focal lengths, like 18-55mm or 55-200mm. Because they can change magnification, ie going from wide to telephoto, they can "zoom" and thus are called zoom lenses. Sometimes, people will talk about a zoom ratio. That's easy to figure out--just take the big number and divide by the smaller number. So the 18-55mm zoom is 55/18 or a 3x zoom. Likewise, the 55-200mm is 200/55 or a 3.6x zoom.
You can also compare lenses: 200/18 or at the 200mm telephoto extension, it is 11x stronger than the other lens at its widest 18mm setting.
Now, what about the aperture or lens opening, sometimes called an f-number or f-stop? Lenses are measured also by how well they let light in. The more light it lets in at the widest aperture, the more expensive the lens is likely to be. You'll see f-numbers like f/2.8, f/3.5, f/4, f/5.6, etc. On zooms, this can vary, so you may see things like f/4.5-5.6.
What this measures is how much light comes in when the lens is at its widest aperture or "wide open." On a zoom, the first number corresponds to the zoom at the wide end; the other number to the zoom at the telephoto (or less wide) end. This is known as a variable aperture zoom.
In dim light, you'll want a lens with a maximum aperture of like f/2.8 or better (smaller number = bigger lens opening) if you want to shoot available light. However, if you shoot with flash, this becomes less critical, which is where consumer level lenses come in. Professionals prefer the wide aperture lenses for a variety of reasons, despite their huge cost.
Aperture affects things like "depth of field" -- the area in focus, which is a whole 'nother discussion entirely.